1. Field of the Invention
This invention relates to apparatus and methods for using Wavefront Coding to improve contrast imaging of objects which are transparent, reflective or vary in thickness or index of refraction.
2. Description of the Prior Art
Most imaging systems generate image contrast through variations in reflectance or absorption of the object being viewed. Objects that are transparent or reflective but have variations in index of refraction or thickness can be very difficult to image. These types of transparent or reflective objects can be considered “Phase Objects”. Various techniques have been developed to produce high contrast images from essentially transparent objects that have only variations in thickness or index of refraction. These techniques generally modify both the illumination optics and the imaging optics and are different modes of what can be called “Contrast Imaging”.
There are a number of different Contrast Imaging techniques that have been developed over the years to image Phase Objects. These techniques can be grouped into three classes that are dependent on the type of modification made to the back focal plane of the imaging objective and the type of illumination method used. The simplest Contrast Imaging techniques modify the back focal plane of the imaging objective with an intensity or amplitude mask. Other techniques modify the back focal plane of the objective with phase masks. Still more techniques, require the use of polarized illumination and polarization-sensitive beam splitters and shearing devices.
Contrast Imaging techniques that require polarizers, beam splitters and beam shearing to image optical phase gradients, we call “Interference Contrast” techniques. These techniques include conventional Differential Interference Contrast (Smith, L. W., Microscopic interferometry, Research (London), 8:385–395, 1955), improvements using Nomarski prisms (Allen, R. D., David, G. B, and Nomarski, G, The Zeiss-Nomarski differential interference equipment for transmitted light microscopy, Z. Wiss. Mikrosk. 69:193–221, 1969), the Dyson interference microscope (Born and Wolf, Principals of Optics, Macmillan, 1964), the Jamin-Lebedeff interferometer microscopes as described by Spencer in 1982 (“Fundamentals of Light Microscopy”, Cambridge University Press, London), and Mach-Zehnder type interference microscopes (“Video Microscopy”, Inoue and Spring, Plenum Press, New York, 1997). Other related techniques include those that use reduced cost beam splitters and polarizers (U.S. Pat. No. 4,964,707), systems that employ contrast enhancement of the detected images (U.S. Pat. No. 5,572,359), systems that vary the microscope phase settings and combine a multiplicity of images (U.S. Pat. No. 5,969,855), and systems having variable amounts of beam shearing (U.S. Pat. No. 6,128,127).
FIG. 1 (Prior Art) is a block diagram 100, which shows generally how Interference Contrast Imaging techniques are implemented. This block diagram shows imaging of a Phase Object 110 through transmission, but those skilled in the art will appreciate that the elements could just as simply have been arranged to show imaging through reflection.
Illumination source 102 and polarizer 104 act to form linearly polarized light. Beam splitter 106 divides the linearly polarized light into two linearly polarized beams that are orthogonally polarized. Such orthogonal beams can be laterally displaced or sheared relative to each other. Illumination optics 108 act to produce focussed light upon Phase Object 110. A Phase Object is defined here as an object that is transparent or reflective but has variations in thickness and/or index of refraction, and thus can be difficult to image because the majority of the image contrast typically is derived from variations in the reflectance or absorbtion of the object.
Objective lens 112 and tube lens 118 act to produce an image upon detector 120. Beam splitter 114 acts to remove the lateral shear between the two orthogonally polarized beams formed by beam splitter 106. Beam splitter 114 is also generally adjustable. By adjusting this beam splitter a phase difference between the two orthogonal beams can be realized. Analyzer 116 acts to combine the orthogonal beams by converting them to the same linear polarization. Detector 122 can be film, a CCD detector array, a CMOS detector, etc. Traditional imaging, such as bright field imaging, would result if polarizer and analyzer 104 and 116 and beam splitters 106 and 114 were not used.
FIG. 2 (Prior Art) shows a description of the ray path and polarizations through the length of the Interference Contrast imaging system of FIG. 1. The lower diagram of FIG. 2 describes the ray path while the upper diagram describes the polarizations. The illumination light is linearly polarized after polarizer 204. This linear polarization is described as a vertical arrow in the upper diagram directly above polarizer 204. At beam splitter 206 the single beam of light becomes two orthogonally polarized beams of light that are spatially displaced or sheared with respect to each other. This is indicated by the two paths (solid and dotted) in both diagrams. Notice that the two polarization states of the two paths in the top diagram are orthogonally rotated with respect to each other. Beam splitter 214 spatially combines the two polarizations with a possible phase offset or bias. This phase bias is given by the parameter Δ in the upper plot. By laterally adjusting the second beam splitter 214 the value of the phase bias Δ can be changed. A Nomarski type prism is described by the ray path diagram, although a Wollaston type prism could have been used as well. Analyzer 216 acts to convert the orthogonal component beams to linearly polarized light. The angle between the polarizer 204 and analyzer 216 can typically be varied in order to adjust the background intensity. Image plane 218 acts to display or record a time average intensity of the linearly polarized light, the sheared component possibly containing a phase shift. This image plane can be an optical viewing device or a digital detector such as CCD, CMOS, etc.
The interactions of the polarizers, beam splitters, and Phase Objects of the Interference Contrast imaging systems have been studied in great detail. For additional background information see “Confocal differential interference contrast (DIC) microscopy: including a theoretical analysis of conventional and confocal DIC imaging”, Cogswell and Sheppard, Journal of Microscopy, Vol 165, Pt 1, January 1992, pp 81–101.
In order to understand the relationship between the object, image, and phase shift Δ consider an arbitrary spatially constant object that can be mathematically described as:Obj=a exp(jθ), where j=√{square root over (−1)}where “a” is the amplitude and θ is the object phase. If the two component beams of the system of FIG. 2 have equal amplitude, and if the component beams are subtracted with relative phases +/−Δ/2 then just after analyzer 216 the resulting image amplitude is given by:amp=a exp(j[θ−Δ/2])−a exp(j[θ+Δ/2])=2j a exp(jθ) sin(Δ/2)
The image intensity is the square of the image amplitude. The intensity of this signal is then given by:int0=4a2 sin(Δ/2)2.
The image intensity is independent of the object phase θ. The phase difference or bias between the two orthogonal beams is given by Δ and is adjusted by lateral movement of the beam splitter, be it a Wollaston or a Nomarski type. If instead of a spatially constant object, consider an object whose phase varies by Δφ between two laterally sheared beams. This object phase variation is equivalent to a change in the value of the component beam phases of Δ. If the component beam phases Δ is equal to zero (no relative phase shift) then the resulting image intensity can be shown to have increases in intensity for both positive and negative variations of object phase. If the component beam bias is increased so that the total phase variation is always positive, the change in image intensity then increases monotonically throughout the range Δφ. The actual value of the change in image intensity with object phase change Δφ can be shown to be:Int1=4a2Δφ sin(Δ).
Interference Contrast imaging the phase bias Δ determines the relative strengths with which the phase and amplitude information of the object will be displayed in the image. If the object has amplitude variations these will be imaged according to int0 above. At a phase bias of zero (or multiple of 2 pi ) the image will contain a maximum of phase information but a minimum of amplitude information. At a phase bias of pi the opposite is true, with the image giving a maximum of amplitude information of the object and a minimum of phase information. For intermediate values of phase bias both phase and amplitude are imaged and the typical Interference Contrast bias relief image is produced, as is well known.
Variation of the phase bias can be shown to affect the parameters of image contrast, linearity, and signal-to-noise ratio (SNR) as well. The ratio of contrast from phase and amplitude in Interference Contrast imaging can be shown to be given by:[contrast due to phase/contrast due to amplitude]=2cot(Δ/2)
The overall contrast in the Interference Contrast image is the ratio of the signal strength to the background and can be shown to be given by:overall contrast=2Δφ cot(Δ/2).
The linearity between the image intensity and phase gradients in the object can be described by:L=[(1+sin(Δ))(2/3)]/[2cos(Δ)].
The signal-to-noise ratio (SNR), ignoring all sources of noise except shot noise on the background, can be shown to be given bySNR=4a cos(Δ/2).
In Interference Contrast imaging systems the condenser aperture can be opened to improve resolution, although in practice, to maintain contrast, the condenser aperture is usually not increased to full illumination. Imaging is typically then partially coherent. Description of the imaging characteristics for Interference Contrast imaging therefore needs to be expressed in terms of a partially coherent transfer function. The partially coherent transfer function (or transmission cross-coefficient), given as C(m,n;p,q), describes the strength of image contributions from pairs of spatial frequencies components m; p in the x direction and n; q in the y direction (Born and Wolf, Principals of Optics, Macmillan, 1975, p. 526). The intensity of the image in terms of the partially coherent transfer function image can be written as:I(x,y)=ƒƒƒƒT(m,n)T(p,g)*C(m,n;p,q) exp(2 pi j[(m−p)x+(n−q)y])dm dn dp dqwhere the limits of integration are + infinity to − infinity. The term T(m,n) is the spatial frequency content of the object amplitude transmittance t(x,y):T(m,n)=ƒƒt(x,y) exp(2 pi j[mx+ny])dx dywhere again the limits of integration are +infinity to −infinity. ( )* denotes complex conjugate. When the condenser aperture is maximally opened and matched to the back aperture or exit pupil of the objective lens, the partially coherent transfer function reduces to (Intro. to Fourier Optics, Goodman, 1968, pg. 120):C(m,n;p,q)=δ(m−n)δ(p−q)[a cos(ρ)−ρsqrt{(1−ρ2 )}]where ρ=sqrt(m2+p2) and δ(x)=1 if x=0, δ(x)=0 otherwise.
The effective transfer function for the Interference Contrast imaging system can be shown to be given as:C(m,n;p,q)eff=2C(m,n;p,q){cos[2 pi(m−n)Λ]−cos(Δ) cos([2 pi(m+n)Λ]−sin(Δ)sin[2 pi (m+p)Λ]}where Λ is equal to the lateral shear of the beam splitters and C(m,n;p,q) is the partially coherent transfer function of the system without Interference Contrast modifications.
Interference Contrast imaging is one of the most complex forms of imaging in terms of analysis and design. These systems are also widely used and studied. But, there is still a need to improve Interference Contrast Imaging of Phase Objects by increasing the depth of field for imaging thick objects, as well as for controlling focus-related aberrations in order to produce less expensive imaging systems than is currently possible.